We conjecture that \(\mathcal {N}\) LEEP outperforms LEEP mainly because GMMs calibrate the posterior probabilities better than the checkpoints' softmax classifiers. The checkpoint ranking quality of LEEP score hinges on the performance of the `dummy classifier' – \(P(y|x,\theta ,t)\) , and \(\theta (x)_z\)  is the key element to calculate it. However, \(\theta (x)\)  can be poorly calibrated [1]} and it can not represent a true probability. In contrast, \(P(v|x)\)  used in \(\mathcal {N}\) LEEP is indeed the probability that the sample belongs to one cluster from a mixture of Gaussian distributions and it can remedy the poor-calibrated problem in LEEP.
